On the lossless-join decomposition of relation scheme(s) in a fuzzy relational data model

A bad model design can be remedied, in many cases by decomposing a relation scheme into a number of simpler schemes. It is desirable to have a lossless-join decomposition which guarantees that there is little information loss when the original relation is recovered from the resultant relations. To obtain a complete information recovery, the authors restrict the extended algebraic operations for base relations to be performed only on the identical elements, and then introduce the notion of identical functional dependency, although those operations for closeness evaluation are performed generally on close elements. This enables adoption of the classical testing algorithm and related results into the fuzzy model in a straightforward manner